The 24-year-old joined the Dutch side from Borussia Monchengladbach in 2015 but has been limited to nine league appearances this season.
Younes, who played the full match for Ajax in their Europa League final defeat to Manchester United last year, sees his contract expire at the end of the campaign.
According to Football Italia, which cites Sky Sport Italia and Mediaset, the Premier League strugglers have offered Ajax €10m (£8.8m) for the Germany international as Carlos Carvalhal seeks to strengthen his team.
However, the report goes on to claim that Younes has rejected a move to the Liberty Stadium as he would prefer a switch to Serie A high-flyers Napoli at the end of the season.
Younes has made 96 appearances for the Amsterdam giants, scoring 17 goals and registering 24 assists.